Let z 1 = 2 + 3 i and z 2 = 3 + 4 i . The set S = z ∈ C : z - z 1 2 - z - z 2 2 = z 1 - z 2 2…

Let z1=2+3i and z2=3+4i. The set S=z∈C:z-z12-z-z22=z1-z22 represents a

  1. straight line with sum of its intercepts on the coordinate axes equals 14
  2. hyperbola with the length of the transverse axis 7
  3. straight line with the sum of its intercepts on the coordinate axes equals -18
  4. hyperbola with eccentricity 2

Solution

Given,

z1=2+3i and z2=3+4i and the set

S=z∈C:z-z12-z-z22=z1-z22,

Now putting the value of z=x+iy, z1=2+3i and z2=3+4i in z-z12-z-z22=z1-z22 we get,

⇒(x-2)2+(y-3)2-(x-3)2-(y-4)2=1+1

⇒   x+y=7

Which is a straight line with intercept 7 on x & y axis, so sum of intercept will be 7+7=14.

Asked in: JEE Main 2023 (25 Jan Shift 1)

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